A spring has a natural length of 25 meters. A force of 12 newtons is required to stretch the spring to a length of 30 meters. How much work is done to stretch the spring from it's natural length?
To find the work done to stretch the spring from its natural length, we need to calculate the change in potential energy.
The potential energy stored in a spring is given by the formula:
PE = (1/2)kx^2
where PE is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.
In this case, the spring is stretched from its natural length, so the displacement x is equal to 30 - 25 = 5 meters.
We know that a force of 12 newtons is required to stretch the spring to a length of 30 meters. This force is equal to the force constant multiplied by the displacement:
F = kx
So we can rearrange the equation to find the spring constant:
k = F / x
k = 12 N / 5 m
k = 2.4 N/m
Now that we have the spring constant, we can calculate the potential energy:
PE = (1/2)kx^2
PE = (1/2)(2.4 N/m)(5 m)^2
PE = (1/2)(2.4 N/m)(25 m^2)
PE = 1.2 N/m * 25 m^2
PE = 30 N*m = 30 Joules
Therefore, the work done to stretch the spring from its natural length is 30 Joules.